Competing orders, nonlinear sigma models, and topological terms in quantum magnets

By T. Senthil, M. Fisher. 2005

159 citations recorded by the source corpus.

A number of examples have demonstrated the failure of the Landau-Ginzburg-Wilson(LGW) paradigm in describing the competing phases and phase transitions of two dimensional quantum magnets. In this paper we argue that such magnets possess field theoretic descriptions in terms of their slow fluctuating orders provided certain topological terms are included in the action. These topological terms may thus be viewed as what goes wrong within the conventional LGW thinking. The field theoretic descriptions we develop are possible alternates to the popular gauge theories of such non-LGW behavior. Examples that are studied include weakly coupled quasi-one dimensional spin chains, deconfined critical points in fully two dimensional magnets, and two component massless $QED_3$. A prominent role is played by an anisotropic O(4) non-linear sigma model in three space-time dimensions with a topological theta term. Some properties of this model are discussed. We suggest that similar sigma model descriptions might exist for fermionic algebraic spin liquid phases.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/c3616b0b7eab7ad03dc94c1c5918e1b32de2741f

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In Atomic and Molecular Physics, and Optics

1. T. Senthil
2. Chong Wang
3. A. Nahum
4. Ashvin Vishwanath
5. Cenke Xu
6. M. Metlitski
7. E. Witten
8. N. Seiberg

In Condensed Matter Physics

1. Chong Wang
2. T. Senthil
3. Cenke Xu
4. A. Nahum
5. Ashvin Vishwanath
6. M. Metlitski
7. S. Sachdev
8. E. Witten

Citations in the corpus

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect (2012, background): “[33] show that the field theory described above at 1⁄4 maps onto the self-dual easy-plane noncompact CP(1) (NCCP(1)) model.”
• Deconfined quantum critical points: symmetries and dualities (2017, methodology): “The most we know about this theory if we want to formulate it directly in terms of the physical bosons is that it has the structure of an (anisotropic) O(4) sigma model at θ = π [27] discussed in Sec.”
• Generalized Symmetries in Condensed Matter (2022, unknown): “There is a sense in which the degrees of freedom of the critical theory are simply the order parameters of both of the neighboring phases, coupled by a WZW term (121, 122).”